Shedding light on the MRI driven dynamo in a stratified shearing box

We study the magneto-rotational instability (MRI) driven dynamo in a geometrically thin disc ($H/R\ll 1$) using stratified zero net flux (ZNF) shearing box simulations. We find that mean fields and EMFs oscillate with a primary frequency $f_{\rm dyn} = 0.017$ ($\approx 9$ orbital period), but also have higher harmonics at $3f_{\rm dyn}$. Correspondingly, the current helicity, has two frequencies $2f_{\rm dyn}$ and $4f_{\rm dyn}$ respectively, which appear to be the beat frequencies of mean fields and EMFs as expected from the magnetic helicity density evolution equation. Further, we adopt a novel inversion algorithm called the `Iterative Removal Of Sources' (IROS), to extract the turbulent dynamo coefficients in the mean-field closure using the mean magnetic fields and EMFs obtained from the shearing box simulation. We show that an $\alpha-$effect ($\alpha_{yy}$) is predominantly responsible for the creation of the poloidal field from the toroidal field, while shear generates back a toroidal field from the poloidal field; indicating that an $\alpha-\Omega$-type dynamo is operative in MRI-driven accretion discs. We also find that both strong outflow ($\bar{v}_z$) and turbulent pumping ($\gamma_z$ ) transport mean fields away from the mid-plane. Instead of turbulent diffusivity, they are the principal sink terms in the mean magnetic energy evolution equation. We find encouraging evidence that a generative helicity flux is responsible for the effective $\alpha$-effect. Finally, we point out potential limitations of horizontal ($x-y$) averaging in defining the `mean' on the extraction of dynamo coefficients and their physical interpretations.